Kuhn-Tucker method

[asd]

How I can maximize this problem using the KKT method?

$\displaystyle f(u,z,l)=\sqrt[ ]{(xz)^2+l^2}$

with the next conditions:

$\displaystyle \displaystyle\frac{x}{3}+\displaystyle\frac{z}{2}+l=24$
$\displaystyle x\geq{0}$;$\displaystyle z\geq{0}$;$\displaystyle l>o$
$\displaystyle x+z>0$

I do the next lagrangian:

$\displaystyle L=-(xz)^2-l^2+a(\displaystyle\frac{x}{3}+\displaystyle\frac{z}{2}+l-24)+b(-x-z)$

and then I have the KKT conditions:

$\displaystyle -2xz^2+\displaystyle\frac{a}{3}-b\geq{0}$ $\displaystyle (-2xz^2+\displaystyle\frac{a}{3}-b)x=0$
$\displaystyle -2x^2z+\displaystyle\frac{a}{2}-b\geq{0}$ $\displaystyle (-2x^2z+\displaystyle\frac{a}{2}-b)z=0$
$\displaystyle -2l+a\leq{0}$ $\displaystyle (-2l+a)l=0$
$\displaystyle \displaystyle\frac{x}{3}+\displaystyle\frac{z}{2}+l-24=0$ $\displaystyle (\displaystyle\frac{x}{3}+\displaystyle\frac{z}{2}+l-24)a=0$
$\displaystyle -x-z\leq{0}$ $\displaystyle (-x-z)b=0$

But then I don't know how to get the solutions.

Thanks

 

[Denis]

http://www.sosmath.com/CBB/viewtopic.php?t=50776